Is the argument over the Danish cartoons really reducible to a matter of free speech? Even if we believe that free speech is a fundamental value, that does not give us carte blanche to say what we like in any context, regardless of consequence or effect. Respect for others, especially in an increasingly interdependent world, is a value of at least equal importance.

Europe has never had to worry too much about context or effect because for around 200 years it dominated and colonised most of the world. Such was Europe's omnipotence that it never needed to take into account the sensibilities, beliefs and attitudes of those that it colonised, however sacred and sensitive they might have been. On the contrary, European countries imposed their rulers, religion, beliefs, language, racial hierarchy and customs on those to whom they were entirely alien. There is a profound hypocrisy - and deep historical ignorance - when Europeans complain about the problems posed by the ethnic and religious minorities in their midst, for that is exactly what European colonial rule meant for peoples around the world. With one crucial difference, of course: the white minorities ruled the roost, whereas Europe's new ethnic minorities are marginalised, excluded and castigated, as recent events have shown.

But it is no longer possible for Europe to ignore the sensibilities of peoples with very different values, cultures and religions. First, western Europe now has sizeable minorities whose origins are very different from the host population and who are connected with their former homelands in diverse ways. If European societies want to live in some kind of domestic peace and harmony - rather than in a state of Balkanisation and repression - then they must find ways of integrating these minorities on rather more equal terms than, for the most part, they have so far achieved. That must mean, among other things, respect for their values. Second, it is patently clear that, globally speaking, Europe matters far less than it used to - and in the future will count for less and less. We must not only learn to share our homelands with people from very different roots, we must also learn to share the world with diverse peoples in a very different kind of way from what has been the European practice.

Europe has little experience of this, and what experience it has is mainly confined to less than half a century. Old attitudes of superiority and disdain - dressed up in terms of free speech, progress or whatever - are still very powerful. Nor - as many liberals like to think - are they necessarily in decline. On the contrary, racial bigotry is on the rise, even in countries that have previously been regarded as tolerant. The Danish government depends for its rule on a racist, far-right party that gained 13% of the seats in the last election. The decision of Jyllands-Posten to publish the cartoons - and papers in France, Germany, Italy and elsewhere to reprint them - lay not so much in the tradition of free speech but in European contempt for other cultures and religions: it was a deliberate, calculated insult to the beliefs of others, in this case Muslims.

This kind of mentality - combining Eurocentrism, old colonial attitudes of supremacism, racism, provincialism and sheer ignorance - will serve our continent ill in the future. Europe must learn to live in and with the world, not to dominate it, nor to assume it is superior or more virtuous. Any continent that has inflicted such brutality on the world over a period of 200 years has not too much to be proud of, and much to be modest and humble about - though this is rarely the way our history is presented in Britain, let alone elsewhere. It is worth remembering that while parts of Europe have had free speech (and democracy) for many decades, its colonies were granted neither. But when it comes to our "noble values", our colonial record is always written out of the script.

This attitude of disdain, of assumed superiority, will be increasingly difficult to sustain. We are moving into a world in which the west will no longer be able to call the tune as it once did. China and India will become major global players alongside the US, the EU and Japan. For the first time in modern history the west will no longer be overwhelmingly dominant. By the end of this century Europe is likely to pale into insignificance alongside China and India. In such a world, Europe will be forced to observe and respect the sensibilities of others.

Few in Europe understand or recognise these trends. A small example is the bitter resistance displayed on the continent to the proposed takeover of Arcelor by Mittal Steel: at root the opposition is based on thinly disguised racism. But Europe had better get used to such a phenomenon: takeovers by Indian and Chinese firms are going to become as common as American ones. A profound parochialism grips our continent. When Europe called the global tune it did not matter, because what happened in Europe translated itself into a global trend and a global power. No more: now it is simply provincialism.

When Europe dominated, there were no or few feedback loops. Or, to put it another way, there were few, if any, consequences for its behaviour towards the non-western world: relations were simply too unequal. Now - and increasingly in the future - it will be very different. And the subject of these feedback loops, or consequences, will concern not just present but also past behaviour.

For 200 years the dominant powers have also been the colonial powers: the European countries, the US and Japan. They have never been required to pay their dues for what they did to those whom they possessed and treated with contempt. Europeans have treated this chapter in their history by choosing to forget. So has Japan, except that in its case its neighbours have not only refused to forget but are also increasingly powerful. As a consequence, Japan's present and future is constantly stalked by its history. This future could also lie in wait for Europe. We might think the opium wars are "simply history"; the Chinese (rightly) do not. We might think the Bengal famine belongs in the last century, but Indians do not.

Europe is moving into a very different world. How will it react? If something like the attitude of the Danes prevails - a combination of defensiveness, fear, provincialism and arrogance - then one must fear for Europe's ability to learn to live in this new world. There is another way, but the signs are none too hopeful.

· Martin Jacques is a senior visiting research fellow at the Asia Research Institute, National University of Singapore